The term 'coder' does seem a bit reductive for the amount of concepts necessary to be a developer. It could also be accurate depending on the developer and the organizational expectations. The developer could be only interested in translating what they are told verbatim into machine code. The organization could also have a micro-managing culture which makes them see developers simply as verbatim code translators. This would also lead the developers working there to look at themselves the same way. As "coders". Seems like this would be the case in a show like Silicon Valley, although I haven't seen it. I did watch a little Halt and Catch Fire and there was a definite executive-enforced "coder" ethos there.
However, I have answered to a lot worse than "coder" before. And I probably wouldn't correct anyone (friends, co-workers in other departments) describing me that way. Without experience in a specific job (any job), humans automatically invent a simple mental model of what that job involves. Just enough to interact with someone in that role on a surface level. Think of your interactions with the accounting department. :)
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